The Effect of the Range of a Modulating Phase Mask on the Retrieval of a Complex Object from Intensity Measurements

Abstract In many fields of science, it is often impossible to preserve the information about the phase of the electromagnetic field, and only the information about the magnitude is available. This is known as the phase problem. Various algorithms have been proposed to recover the information about phase from intensity measurements. Nowadays, iterative algorithms of phase retrieval have become popular. Many of these algorithms are based on modulating the object under study with several masks and retrieving the missing information about the phase of an object by applying mathematical optimization methods. Several of these algorithms are able to retrieve not only the phase but also the magnitude of the object under study. In this study, we investigate the effect of the range of modulation of a mask on the accuracy of the retrieved magnitude and phase map. We conclude that there is a sharp boundary of the range of modulation separating the successfully retrieved magnitude and phase maps from those retrieved unsuccessfully. A decrease in the range of modulation affects the accuracy of the retrieved magnitude and phase map differently.

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Image Reconstruction From TEM Diffraction Patterns Using Feinup Algorithm

Microscopy and Microanalysis ◽

10.1017/s1431927600032669 ◽

2000 ◽

Vol 6 (S2) ◽

pp. 34-35

Author(s):

Q. Chen ◽

U. Weierstall ◽

J. C. H. Spence

Keyword(s):

Image Reconstruction ◽

A Priori ◽

Iterative Algorithms ◽

Simulated Data ◽

Super Resolution ◽

Complex Object ◽

X Rays ◽

Phase Problem ◽

Support Functions ◽

Diffraction Patterns

Iterative algorithms, which use diffracted intensities and some a-priori knowledge of an image to solve the phase problem, have been under development for many years. The promised super-resolution images, reconstructed from diffraction information alone, would be of the greatest value for molecular imaging and for the image of nonperiodic structures in materials. Using simulated data it is possible, for example, to reconstruct a complex object from a knowledge of its diffracted intensities with certain known support functions. Some success has recently been achieved reconstructing micrometer-sized non-periodic objects using coherent X-rays by the Feinup method. One favorable support function consists of two holes spanned by the coherence width of the beam, with one or both holes containing an unknown object. Our simulations, which iterate between diffracted intensities and the image, applying the known support (either completely opaque or completely transparent) and intensities in each domain, confirm that image reconstruction is possible for loose supports and noiseless data.

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A More Effective Formulation of the Path Generation Mechanism Synthesis Problem

23rd Biennial Mechanisms Conference: Mechanism Synthesis and Analysis ◽

10.1115/detc1994-0200 ◽

1994 ◽

Author(s):

Irfan Ullah ◽

Sridhar Kota

Keyword(s):

Objective Function ◽

Error Function ◽

Mathematical Optimization ◽

Optimization Methods ◽

Complex Nature ◽

Mechanism Synthesis ◽

Structural Error ◽

Crank Angle ◽

The Common ◽

Selection Of

Abstract Use of mathematical optimization methods for synthesis of path-generating mechanisms has had only limited success due to the very complex nature of the commonly used Structural Error objective function. The complexity arises, in part, because the objective function represents not only the error in the shape of the coupler curve, but also the error in location, orientation and size of the curve. Furthermore, the common introduction of timing (or crank angle), done generally to facilitate selection of corresponding points on the curve for calculating structural error, has little practical value and unnecessarily limits possible solutions. This paper proposes a new objective function, based on Fourier Descriptors, which allows search for coupler curve of the desired shape without reference to location, orientation, or size. The proposed objective function compares overall shape properties of curves rather than making point-by-point comparison and therefore does not requires prescription of timing. Experimental evidence is provided to show that it is much easier to search the space of the proposed objective function compared to the structural error function.

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Optimal Design of Composite Lightweight Rollers

19th Design Automation Conference: Volume 2 — Design Optimization; Geometric Modeling and Tolerance Analysis; Mechanism Synthesis and Analysis; Decomposition and Design Optimization ◽

10.1115/detc1993-0386 ◽

1993 ◽

Author(s):

K. Bellendir ◽

Hans A. Eschenauer

Keyword(s):

Structural Analysis ◽

Shell Theory ◽

Analytical Procedure ◽

Mathematical Optimization ◽

Optimization Methods ◽

Analysis Procedure ◽

Various Boundary Conditions ◽

Evaluation Models ◽

Laminate Theory ◽

Static Behaviour

Abstract A well-aimed layout of fibre-reinforced lightweight rollers does not only require an efficient structural analysis procedure but also the application of structural optimization methods. Therefore, an analytical procedure is introduced for the calculation of the static behaviour of cylindrical shells subject to axisymmetric and/or nonaxisymmetric loads. In the scope of this procedure, arbitrary, unsymmetrical laminates as well as various boundary conditions will be considered. Basis is the shell theory by Flügge enhanced by anisotropic constitutive equations (material law) in the scope of the classical laminate theory. By means of mathematical optimization procedures we then determine optimal lightweight rollers, using different design and evaluation models. For that purpose, coated and uncoated roller constructions as well as hybrid types made of CFRP/GFRP will be applied. Concluding, we will discuss possible improvements and advantages of anisotropic lightweight rollers in contrast to isotropic ones made of steel or aluminium.

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Newer Mathematical Optimization Methods

Design and Optimization of Metal Structures ◽

10.1533/9781782420477.7 ◽

2008 ◽

pp. 7-19

Author(s):

József Farkas ◽

Károly Jármai

Keyword(s):

Mathematical Optimization ◽

Optimization Methods

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Two-Step Phase Retrieval Algorithm Using Single-Intensity Measurement

International Journal of Optics ◽

10.1155/2018/8643819 ◽

2018 ◽

Vol 2018 ◽

pp. 1-7

Author(s):

Cheng Zhang ◽

Meiqin Wang ◽

Qianwen Chen ◽

Dong Wang ◽

Sui Wei

Keyword(s):

Phase Retrieval ◽

Fourier Spectrum ◽

Retrieval Algorithm ◽

Improved Method ◽

Retrieval Method ◽

Intensity Measurements ◽

Successful Recovery ◽

Reconstruction Quality ◽

Low Probability ◽

Phase Retrieval Algorithm

Aiming at the problem that the single-intensity phase retrieval method has poor reconstruction quality and low probability of successful recovery, an improved method is proposed in this paper. Our method divides the phase retrieval into two steps: firstly, the GS algorithm is used to recover the amplitude in the spatial domain from the single-spread Fourier spectrum, and then the classical GS algorithm using two intensity measurements (one is recorded and the other is estimated from the first step) measurements is used to recover the phase. Finally, the effectiveness of the proposed method is verified by numerical experiments.

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The Optimum Alignment of Marine Shafting

Marine Technology and SNAME News ◽

10.5957/mt1.1974.11.3.260 ◽

1974 ◽

Vol 11 (03) ◽

pp. 260-269

Author(s):

Ronald T. Bradshaw

Keyword(s):

United States ◽

Mathematical Optimization ◽

Implementation Process ◽

Optimization Methods ◽

The United States ◽

Journal Bearings ◽

Practical Realization ◽

Shaft System ◽

Economic Basis ◽

Optimum Alignment

Alignment of marine shafting generally implies a judicious misalignment of the supporting bearings in order to achieve acceptable values of bearing reactions and shaft stresses. To achieve a true optimum it is necessary to describe quantitatively the desirable features of an alignment, and a combined technical/economic basis for this description is presented. The result is a well-defined problem that is solved by mathematical optimization methods. Results of the procedure are illustrated by alignment plans derived for, and adopted by, ships recently built in the United States and abroad. The practical realization of an alignment plan is discussed and means of speeding up the implementation process are proposed. Improvements in the elastic representation of the shaft system are described and the question of hydrodynamic support in journal bearings is considered. Discussers: Technical Staff, ABSP. F. Nuclo C. L. Stahly

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Application of Differential Evolution Algorithm in Transmission Expansion Planning

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.394.314 ◽

2013 ◽

Vol 394 ◽

pp. 314-320

Author(s):

Ibrahim Al Hamrouni ◽

Azhar Khairuddin ◽

M. Salem

Keyword(s):

Differential Evolution ◽

Heuristic Method ◽

Differential Evolution Algorithm ◽

Mathematical Optimization ◽

Minimum Cost ◽

Optimization Methods ◽

Expansion Planning ◽

Transmission Expansion Planning ◽

Transmission Expansion ◽

Evolution Algorithm

Transmission expansion planning has become a complicated procedure more than it was. The rapid growth of the transmission networks and the deregulation has introduced more objectives and uncertainties to the transmission network planners. As a result of that, new approach and criteria that can replace the old ones are needed for TEP problem. The main goal of this process is to locate the additional transmission lines that must be added to meet the forecasted load in the system adequately with minimum cost. There have been several methods applied for this purpose; mathematical optimization methods, heuristic and Meta heuristic methods. This paper reviews the use of Meta heuristic method by the means of differential evolution algorithm (DEA) to solve this multi objective optimization problem. In addition, some suggestions have been made by the author that can make the DEA more efficient and applicable in the real world networks.

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